A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Concept explainers

Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear re…
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Topic Video
Question
  • A game that draws 3 digits from 0-9 from three separate machines.
    • What is the probability of winning a “straight” bet by matching the three digits in the exact order?
    • What is the probability of winning a “box” bet by matching the three digits in any order?
    • What is the probability of not matching any numbers on a ticket?
  • A game that draws 4 digits from 0-9 from four separate machines.
    • What is the probability of winning a “straight” bet by matching the four digits in the exact order?
    • What is the probability of winning a “box” bet by matching the four digits in any order?
    • What is the probability of not matching any numbers on a ticket?
  • A game that draws 5 digits from 1-49 from the same machine. In other words, numbers are drawn and not replaced.
    • What is the probability of winning the jackpot by matching all 5 numbers?
    • What is the probability of winning a major prize by matching 4 of the 5 numbers? Make the calculation assuming the first 4 values are matched and the fifth one does not.
    • What is the probability of not matching any numbers on a ticket?
  • A super-mega-jackpot game that draws 6 numbers from 1 – 70 from a single machine and then a Super-Mega-Match ball numbered 1 – 30 from a separate machine.
    • What is the probability of winning the Super-Mega jackpot by matching all six numbers and the Super-Mega-Match ball?
    • What is the probability of winning the jackpot by matching all six numbers, but not matching the Super-Mega-Match ball?
    • What is the probability of not matching any numbers on a ticket?
  • State-run lottery games tend to pay out 50% of what the odds against winning are, rounded up. For instance, if the odds against winning in a game are 499: 1, the lottery game will pay $250 for a winning $1 ticket. This is how the lottery raises money for the state. Complete the table below with predicted payout values for winning $1 bets using this formula.

 

3-Digit Drawing 4-Digit Drawing 5-Number Drawing Super-Mega Drawing
Straight win: Straight win: Match 5: Super-Mega Jackpot
Boxed win: Boxed win:  Match 4: Jackpot:

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